Hagrid introducing Grawp
Book: While Ron is away during a Quidditch match, Hagrid leads Harry and Hermione into the Forbidden Forest, where he introduces them to his brother Grawp and asks them to take care of him in his absence in case Umbridge fires him.
Movie: Hagrid searches out Harry, Ron, and Hermione in the school, where he leads all three in the forest and asks them the same question.
Rita Skeeter and the Quibbler
Book: Hermione blackmails her to write an article in the Quibbler, to help Harry's image in the media.
Movie: Rita and her article do not make an appearance in the film, and the Quibbler is of no importance, though it does make a brief appearance.
Book: After the attack upon Mr. Weasley in the Department of Mysteries, Harry and the Weasley children return to Grimmauld Place and visit Mr. Weasley at St. Mungo's. Here they see Neville visiting his parents, and encounter Professor Lockhart.
Movie: The visit to St. Mungo's is missing from the film. Instead, Neville tells Harry about his parents in the Room of Requirement after Bellatrix Lestrage breaks out.
Sybill Trelawney's Defense / The appointment of Firenze
Book: During the shouting match between Trelawney and Dolores Umbridge, with Umbridge attempting to expel Trelawney from Hogwarts, Dumbledore intervenes to defend Trelawney. Dumbledore asks Trelawney to remain in the castle, but her Divinations class is turned over to Firenze.
Movie: Firenze does not appear and is not named to replace Trelawney as Divinations instructor.
Centaur's hostility towards Hogwarts and the Ministry of Magic
Book: Relations between the centaurs and humans have been tense for quite some time, and finally boil over when Firenze accepts Dumbledore's offer to take the Divinations position, as the centaurs see him as a traitor.
Movie: Hagrid tells Harry, Ron, and Hermione that the the Ministry has been taking away vast amounts of land in the Forbidden Forest, thus taking away much of the centaurs' land.
Umbridge and the Dementors
Book: It is eventually revealed that Umbridge set the Dementors on Harry in order to trigger an "illegal use of underage magic" charge, and to discredit Harry.
Movie: It is not mentioned that Umbridge sent the Dementors.
Voldemort's Fake Vision
Book: Harry's fake vision of Sirius Black being tortured in the Prophecy room in the Department of Mysteries happens during his History of Magic O.W.L Exam
Movie: Happens during the Fred and George stunt, which was pulled during the charms O.W.L.
Fred and George
Book: Fred and George cause havoc in school twice before leaving for good (setting off fireworks, then a swamp).
Movie: After disrupting O.W.L.'s with fireworks, Fred and George leave on their brooms.
Sirius' Two-Way Mirror
Book: Sirius gives Harry a Two-Way Mirror as a gift for means of communication between each other initially. However, Harry forgets about the gift and only opens it after Sirius' death.
Movie: Cut from the movie.
Fred and George's Plans for the Joke Shop
Book: The twins plan to create a Joke Shop and finally announces it to everyone at their flight away from Hogwarts. The location is said to everyone, at Diagon Alley. It is also stated that they got the money from Harry after he got the winnings at the Triwizard tornament last year.
Movie: Nothing is stated about their joke shop. They left school, not stating where or what they are going to do, although an earlier scene alludes to the Weasley twins' testing of Puking Pastilles on students.
Umbridge and McGonagall's shouting match after Harry's Career Advice session
Book: Professors Umbridge and McGonagall get into an argument during Harry's Career Advice session with McGonagall. Umbridge enters and begins interrupting their conversation which ends with Umbridge ranting about McGongall wanting Dumbledore as Minister of Magic
Movie: This is not seen or mentioned at all in the film, although McGonagall is seen arguing with Umbridge about her "Medieval" teaching methods
The Woes of Mrs. Weasley
Book: Molly tries to tackle a Boggart and we find that she has the nightmare of losing every member of her family including Harry in a horrific act. Not only does it show Molly's worst fear but Harry is first to overhear her crying with Lupin, Sirius, and Moody coming in to see what is going on, with them reassuring her that the Order is much more prepared than last time, and quickly performing the charm properly.
Movie: This scene was cut from the movie.